Answer:
a) v= 2.1 m/s
b) ω = 0.807 rad/s
Explanation
Conceptual analysis :
The dog and the merry-go- round describes a circular motion, then, the following formulas apply :
[tex]a_{c} =\frac{v^{2} }{r}[/tex] Formula (1)
v = ω *r Formula (2)
Where:
[tex]a_{c}[/tex] : Centripetal acceleration(m/s²)
v: linear speed or tangential (m/s)
r : radius of the circle (m)
ω : angular speed ( rad/s)
Data
r= 2.6 m
[tex]a_{c}[/tex] = 1.7 m/s²
Problem develpment
a) We replace data in the formula 1 to calculate the dog's linear speed(v):
[tex]a_{c} =\frac{v^{2} }{r}[/tex]
[tex]1.7 =\frac{v^{2} }{2.6}[/tex]
[tex]v^{2} =1.7*2.6 = 4.42[/tex]
[tex]v=(\sqrt{4.42})\frac{m}{s}[/tex]
v= 2.1 m/s
b)We replace data in the formula 2 to calculate the angular speed of the merry-go- round (ω).
v = ω *r
2.1 = ω *2.6
ω = 2.1/2.6
ω = 0.807 rad/s
